This invention relates to transmitting digital symbols over a band-limited channel by modulating a carrier in accordance with a sequence of signals selected from an available signal constellation by a coding technique which introduces dependencies between signals in the sequence to increase immunity to noise (i.e., to achieve a so-called "coding gain" compared with an uncoded system).
Csajka et al., U.S. Pat. No. 4,077,021, and Ungerboeck, "Channel Coding with Multilevel/Phase Signals," IEEE Transactions on Information Theory, Vol. IT-28, No 1, January, 1982, incorporated herein by reference, disclose a coding system in which a conventional two-dimensional signal constellation having 2.sup.N signal points (the number needed for simple mapping of symbols having N bits in an uncoded system in which no dependencies are introduced between signal points) is doubled in size to 2.sup.N+1 signal points. An encoder introduces a degree of redundancy by adding one bit of information to each N-bit symbol, based on the state of a finite-state memory in the encoder, and the resulting N+1 bits for each symbol are mapped into one of the 2.sup.N+1 possible signal points in the constellation. The signal points are organized into subsets which are disjointed (i e., have no signal points in common) and arranged so that the minimum distance between two signal points belonging to one subset is greater than the minimum distance between any two signal points in the constellation. The state of the finite state memory is arranged to depend on the subsets from which past signals were drawn. The encoder performs a coding function by using the state of the finite state memory as the basis for determining the subset from which each signal is to be drawn. Because this coding effectively permits only certain sequences of signals to be transmitted, each signal carries (in the form of the identity of the subset from which it is drawn) historical information which is exploited at the receiver to decode the sequence of received signals using a maximum likelihood sequence estimation technique (e.g., one based on the Viterbi Algorithm, as described in Forney, "The Viterbi Algorithm," Proceedings of the IEEE, Vol. 61, No. 3, March, 1973, incorporated herein by reference).
Another coding system, disclosed in copending patent application. U.S. Ser, No. 439,740, Forney, uses a signal constellation having more than 2.sup.N but fewer than 2.sup.N+1 signal points organized into two subsets which are partially overlapping and partially disjointed. A two-state encoder is arranged in such a way that on average only a portion of the sent signals carry historical information (i.e., include redundancy).
Another copending patent application, U.S. Ser. No. 485,069, U.S. Pat. No. 4,597,090 issued 6/24/86, Forney, shows systems in which the symbols to be sent are taken in groups, each having at least two symbols. Each group is encoded independently into a multi-dimensional point corresponding in turn to two or more two-dimensional signal points. The set of multi-dimensional points from which each multi-dimensional point may be drawn is independent of the two-dimensional signal points sent for any other group of symbols, but there is an interdependence among the signal points drawn for a given group.